Hard-to-measure nuclides in decommissioning waste
A waste package leaving a nuclear facility has to be declared nuclide by nuclide, and the declaration has to include nuclides that nothing outside the package can detect. They emit no photon that survives the container, or none at all, and their electrons are stopped within millimetres. The usual name for them is hard-to-measure nuclides, and the usual way of declaring them without opening every drum is the scaling factor: a ratio, established by laboratory analysis of samples, between each of them and a gamma emitter that can be measured from outside. This note sets out what makes them hard, what the ratio assumes, and how fast the ratio changes with time, with the figures computed from the nuclide table.
Nuclides invisible from outside a drum
The table lists the hard-to-measure nuclides most often named in waste declarations from power reactors. Of these 11, 10 have no photon line above 20 keV in this table , and the exception, Cl-36, emits annihilation photons in 0.028 of every hundred decays. The electrons of the beta emitters are stopped by a few millimetres of plastic at most — far less than a steel drum wall. I-129 does emit low-energy photons that this table does not carry; the container and the waste itself absorb most of them.
| Nuclide | Half-life | Decay | Beta endpoint (MeV) | Stopped by acrylic (mm) |
|---|---|---|---|---|
| H-3 | 12.32 years | beta-minus decay | 0.019 | 0.0050 |
| C-14 | 5700 years | beta-minus decay | 0.156 | 0.24 |
| Cl-36 | 3.013 × 10⁵ years | beta-minus decay | 0.710 | 2.2 |
| Ca-41 | 9.94 × 10⁴ years | electron capture | — | — |
| Fe-55 | 2.744 years | electron capture | — | — |
| Ni-59 | 7.6 × 10⁴ years | electron capture with beta-plus | — | — |
| Ni-63 | 100.8 years | beta-minus decay | 0.067 | 0.057 |
| Sr-90 | 28.91 years | beta-minus decay | 0.546 | 1.6 |
| Tc-99 | 2.111 × 10⁵ years | beta-minus decay | 0.297 | 0.65 |
| I-129 | 1.57 × 10⁷ years | beta-minus decay | 0.149 | 0.22 |
| Pu-241 | 14.329 years | beta-minus decay | 0.021 | 0.0062 |
Ranges are Katz–Penfold fits to the endpoint. A dash means the nuclide emits no beta recorded here: Ca-41, Fe-55 and Ni-59 decay by electron capture and give off only X-rays and Auger electrons of a few keV.
The electron-capture nuclides are the hardest case. Fe-55, Ni-59 and Ca-41 emit characteristic X-rays of the daughter element and Auger electrons, at energies low enough that a fraction of a millimetre of water, and much less of steel, absorbs most of them. They are detectable only after the element has been separated chemically and presented to a detector in a thin, uniform form.
Where they come from
Two families of origin decide which gamma emitter a nuclide can be tied to. The activation products are made by neutron capture in the structure of the reactor and its surroundings: Fe-55 from iron-54 and Ni-63 and Ni-59 from nickel-62 and nickel-58 in steel, Co-60 from cobalt-59 present as an impurity in the same steel, C-14 from nitrogen-14 and oxygen-17, Cl-36 from chlorine-35, Ca-41 from calcium-40 in concrete, and H-3 from lithium-6, boron-10 and deuterium. In activated concrete the companion gamma emitters are typically Co-60, Eu-152 and Eu-154, the europium coming from trace europium in the aggregate and cement.
The second family comes from fuel: fission products such as Sr-90, Tc-99, I-129 and Cs-137, and actinides such as plutonium, americium and curium. These reach waste through fuel cladding defects and the contamination that follows, so they travel together with Cs-137 in a way activation products do not. A scaling factor ties a hard-to-measure nuclide to a key nuclide of the same family — Co-60 for activation products, Cs-137 for fission products — because only within a family do the two share a production mechanism and a route into the waste.
Scaling factors
The method is set out in ISO 21238 and in the IAEA report Determination and Use of Scaling Factors for Waste Characterization in Nuclear Power Plants. Samples representative of a waste stream are analysed destructively for both the hard-to-measure nuclide and the key nuclide. The ratios are examined for correlation — a scaling factor is only defensible where the two activities rise and fall together across the samples — and a single factor is derived for the stream, usually as the geometric mean of the sample ratios, because ratios between nuclides of different origin spread over orders of magnitude and are closer to log-normal than to normal. In operation, each package's key nuclide is measured by gamma spectrometry from outside and the hard-to-measure activities are inferred by multiplication.
Where no usable correlation exists, the alternative is a mean activity concentration for the stream, applied to every package regardless of its gamma reading. Both approaches rest on the same premise: that the samples represent the stream, and that the stream does not change in a way the samples did not see.
Ratios that drift with time
A scaling factor is a ratio of two activities that decay at different rates, so it is only true at a stated reference date. Multiplying by e−(λD−λK)t, where the subscripts are the hard-to-measure and key nuclides, carries it to another date. The factors by which common ratios change are below.
| Ratio | After 5 years | After 10 years | After 20 years |
|---|---|---|---|
| Ni-63 / Co-60 | × 1.86 | × 3.48 | × 12.1 |
| C-14 / Co-60 | × 1.93 | × 3.72 | × 13.8 |
| H-3 / Co-60 | × 1.46 | × 2.12 | × 4.50 |
| Fe-55 / Co-60 | × 0.546 | × 0.298 | × 0.0887 |
| Sr-90 / Cs-137 | × 0.995 | × 0.991 | × 0.982 |
| Tc-99 / Cs-137 | × 1.12 | × 1.26 | × 1.59 |
| Pu-241 / Cs-137 | × 0.881 | × 0.776 | × 0.603 |
From the recorded half-lives only. A factor above one means the hard-to-measure nuclide becomes relatively more important.
The activation products show the problem plainly. Co-60 has a half-life of 1925.28 days; Ni-63 has one of 100.8 years. A Ni-63/Co-60 ratio measured at shutdown is 3.5 times larger ten years later and 12 times larger after twenty, and the C-14 ratio grows faster still. Fe-55 moves the other way, falling to 9% of its starting ratio over twenty years. In the fission family the picture is calmer: Sr-90 and Cs-137 have nearly the same half-life, and their ratio moves by less than 2% in twenty years.
The same arithmetic undermines the key nuclide itself on a long project. Twenty years after shutdown Co-60 retains 7.2% of its activity and Ni-63 retains 87%. A drum of activated steel whose activity was mostly Co-60 at shutdown can be mostly Ni-63 two decades later, and the Co-60 reading on which the declaration hangs has by then become small enough that its own uncertainty dominates the inferred values. A scaling factor derived during operation and applied without decay correction late in decommissioning is therefore wrong in a known direction, and wrong by a large factor.
Counting atoms instead of decays
For the longest-lived nuclides a decay counter is the wrong instrument. One becquerel of a nuclide requires T½/ln 2 atoms, so the number of atoms behind each becquerel rises in proportion to the half-life. A becquerel of I-129 is 1.3 × 106 times as many atoms as a becquerel of H-3; the specific activity of I-129 is 6.54 × 106 Bq/g against 3.56 × 1014 Bq/g for H-3. For I-129, Tc-99, Cl-36 and Ca-41 it is often easier to count the atoms than to wait for them to decay, which is why inductively coupled plasma mass spectrometry and accelerator mass spectrometry appear alongside liquid scintillation counting in the methods used for them. The specific activity calculator converts between the two views.
Laboratory methods in outline
- H-3 and C-14 — released from the sample by combustion or digestion, trapped as water and carbon dioxide, and counted by liquid scintillation.
- Fe-55, Ni-63 and Ni-59 — iron and nickel separated chemically; Fe-55 and Ni-63 counted by liquid scintillation, Ni-59 by low-energy X-ray spectrometry or mass spectrometry.
- Sr-90 — strontium separated, then counted directly or through its daughter Y-90 once that has grown back.
- Tc-99, I-129 and Cl-36 — separated as anions and measured by liquid scintillation or mass spectrometry.
- Plutonium, americium and curium — separated and measured by alpha spectrometry, except Pu-241, which is a beta emitter with an endpoint of 20.8 keV and is counted by liquid scintillation.
Every one of these involves chemical separation, which is why the analyses are slow and expensive and why scaling factors exist. The quality of a declaration therefore rests on the quality of a modest number of radiochemical results.
Relevance to disposal
Several of these nuclides combine a long half-life with chemistry that keeps them mobile. C-14, Cl-36 and I-129 tend to be present as anions or as gases, and so does Tc-99 under oxidising conditions; most minerals adsorb anions weakly, so in disposal safety assessments these nuclides are often among those that dominate the calculated long-term dose. Acceptance criteria for disposal facilities limit their inventories for that reason, and an inventory inferred from a drifting scaling factor feeds directly into those limits. How sorption is represented in transport calculations is the subject of the M-Phreefiteq workbench on this platform, which fits surface complexation models to sorption data and runs one-dimensional transport.
Limits of this note
The figures above use half-lives only. They do not say what a scaling factor should be for any plant, which depends on its materials, its operating history and its fuel performance, and is established by measurement. Branching and ingrowth — Pu-241 decaying to Am-241, for instance — add terms that a two-nuclide ratio does not carry.
Where to go next
- Decay calculator — the correction from a scaling factor's reference date to the date of declaration.
- Specific activity — atoms, grams and becquerels for the long-lived nuclides.
- Minimum detectable activity — what limits the gamma measurement of the key nuclide.
- Natural decay series — the other place where what is measured is not what is declared.